Mathematics, 07.03.2020 01:31 jeanieb

Susan Jackson is a long jumper with the University's athletics team. She is currently in training for the next summer Olympic games.

A sample of 51 long jumps have been recorded.

7.4 6.86 6.99 6.81 6.62 7.1 6.94 6.72 6.71 7.28 6.78 6.85 7.13 7.07 6.76 6.99 6.61 7.41 6.27 7.01 6.31 7.18 7.01 6.71 6.39 6.98 6.82 6.98 6.91 6.58 7.11 6.89 6.86 7.01 6.49 6.64 6.91 6.58 7.01 7.23 6.69 7.3 7.33 7.1 6.9 6.85 7.29 6.71 7.09 6.92 6.55

b)Calculate the 95% confidence interval for the mean jump length. Give your answers to 2 decimal places.

Answers: 3

Show answers

Answers

Answer from: tiffanibell71

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=6.894$ represent the sample mean for the sample

s=0.269 represent the sample standard deviation

$6.894-2.008\frac{0.269}{\sqrt{51}}=6.818$

$6.894+2.008\frac{0.269}{\sqrt{51}}=6.970$

So on this case the 95% confidence interval would be given by (6.82;6.97)

Step-by-step explanation:

For this case we have the following data:

7.4 6.86 6.99 6.81 6.62 7.1 6.94 6.72 6.71 7.28 6.78 6.85 7.13 7.07 6.76 6.99 6.61 7.41 6.27 7.01 6.31 7.18 7.01 6.71 6.39 6.98 6.82 6.98 6.91 6.58 7.11 6.89 6.86 7.01 6.49 6.64 6.91 6.58 7.01 7.23 6.69 7.3 7.33 7.1 6.9 6.85 7.29 6.71 7.09 6.92 6.55

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the mean and the deviation from these data with the following formulas:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}$

$\bar X=6.894$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=0.269 represent the sample standard deviation

n=51 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

df=n-1=51-1=50

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,50)".And we see that $t_{\alpha/2}=2.008$

Now we have everything in order to replace into formula (1):

$6.894-2.008\frac{0.269}{\sqrt{51}}=6.818$

$6.894+2.008\frac{0.269}{\sqrt{51}}=6.970$

So on this case the 95% confidence interval would be given by (6.82;6.97)

Answer from: Quest

Look at this and see if it

Answer from: Quest

Bbghjkskxnxnixidnd dbshusjsjsns sndnbs

Another question on Mathematics

Mathematics, 21.06.2019 14:00

Carson has only $20 bills and $10 bill in her wallet. the total value of the bills is $50. she has 1 more $20 bill than $10 bills. how many each kind of bill does carson have? a. one $20 and two $10 bills b. two $20 bills and one $10 bill c. one $20 bills and three $10 bills d. two $20 bills and two $10 bills

Answers: 2

Answer

Mathematics, 21.06.2019 23:30

In order for the function to be linear, what must m be and why? m = 22 because the rate of change is 1. m = 20 because the rate of change is 3. m = 22 because the rate of change is -1. m = 20 because the rate of change is -3.

Answers: 2

Answer

Mathematics, 22.06.2019 00:50

Identify the statement below as either descriptive or inferential statistics. upper a certain website sold an average of 117 books per day last week. is the statement an example of descriptive or inferential statistics? a. it is an example of descriptive statistics because it uses a sample to make a claim about a population. b. it is an example of inferential statistics because it uses a sample to make a claim about a population. c. it is an example of inferential statistics because it summarizes the information in a sample. d. it is an example of descriptive statistics because it summarizes the information in a sample.

Answers: 1

Answer

Mathematics, 22.06.2019 01:00

Asmall book publisher knows that 26 books weigh 41 lbs. how much do 40 books weigh?

Answers: 1

Answer

You know the right answer?

Susan Jackson is a long jumper with the University's athletics team. She is currently in training fo...

Questions